Simulation of reservoir dynamic damage and influencing factors of horizontal wells in heterogeneous carbonate reservoirs

As the development of well types for low permeability reservoirs shifts from vertical to highly inclined/horizontal wells, targeted studies of oil and gas reservoir damage must be conducted for such well types to improve the science and effectiveness of acidification conversion. Taking into account the formation of mud cake and the dynamic damage factors caused by drilling fluid on the reservoir during horizontal well drilling, a refined dynamic description model for nonuniform damage in horizontal wells was established. The coupled simulation accounts for the dynamical destruction of the skin factor of the reservoir and the dynamical generation of the slurry. The coupled model consists of a radial mud cake dynamic formation model, a reservoir damage radius model, a permeability distribution model, and a horizontal well inhomogeneous skin factor model. It captures the dynamic evolution of reservoir damage due to drilling fluid contamination during horizontal well drilling and provides a real‐time representation of changes in the reservoir skin factor of horizontal wells, measuring the depth and extent of radial reservoir damage. Clarifying the extent of reservoir damage and its impact in horizontal well sections can help select appropriate acidification methods, improve acid distribution processes, and ultimately improve the effectiveness of mitigating reservoir damage and increasing oil and gas well productivity.

around the wellbore, creating a widespread damage zone.This causes more severe and complex damage to the reservoir compared to the vertical well, significantly impacting the horizontal well's production.The damage to the reservoir in horizontal wells is intricately linked to the stimulation technology utilized.][7][8][9] Compared to vertical wells, horizontal wells have a larger contact area with the reservoir, and the duration of contact between the drilling fluid, completion fluid, and the reservoir is significantly longer.The pressure difference when drilling into oil and gas reservoirs is greater than that of vertical wells. 10The pore pressure remains consistent for a particular oil and gas reservoir; however, as the horizontal well section expands, the flow resistance of the drilling fluid intensifies, resulting in a direct pressure impact on the oil and gas reservoir.As a result, the pressure difference escalates proportionally with the extension of the horizontal well section, leading to exacerbated damage to the oil and gas reservoir with the rising pressure difference.For these reasons, horizontal wells cause more severe reservoir damage than vertical wells, and the damage zone of horizontal wells cannot be regarded as a simply cylindrical area with reduced permeability.The damage zone's characteristics primarily encompass three aspects [11][12][13] : ① Due to the reservoir's anisotropy, the vertical and horizontal permeabilities along the horizontal well section differ, leading to an elliptical cross-section of the damage zone perpendicular to the wellbore.This elliptical shape is determined by the ratio of vertical to horizontal permeability.② During the drilling and completion process of horizontal wells, the length of the horizontal well section results in varying soaking times for the drilling and completion fluid at different positions.Consequently, the damage zone is more pronounced at the onset of the horizontal section than at its end, leading to an uneven distribution of the damage zone.The heterogeneity of reservoir permeability and porosity is pronounced in different locations within the horizontal well section, with substantial variations in physical properties leading to varying degrees of damage across different horizontal sections.
Numerous scholars have taken into account the permeability anisotropy and the reservoir's exposure time in the working fluid, and they hold the belief that the damage zone in the horizontal section is a consistent elliptical cone-shaped region that varies linearly from the heel to the toe.Nonetheless, they overlook the variability of the permeability and porosity in the horizontal section reservoir.If the horizontal section's physical properties vary significantly, the elliptical cone's change may not necessarily be linear.Frick and Economides et al. 14 hypothesized that the contamination zone in the horizontal well takes the form of an elliptical cone, with the larger end located near the heel of the horizontal well, taking into account the anisotropy of the reservoir.They then calculated the distribution of the nearwellbore formation contamination zone along the horizontal section of the wellbore and derived the formula for the equivalent skin factor of the horizontal well. 14The findings indicate a considerable variation in the extent of the contamination zone across different locations within the horizontal section.Yuan et al. derived an empirical formula for calculating the damage depth of drilling fluid in horizontal wells based on experimental data. 15Ajay established a multicomponent filtration model for solid particles, which considered the influence of different grades of solid particles on the filtration process in the same system, which can predict the damage depth of drilling fluid and optimize the distribution of solid particles. 16Parn-anurak et al. established a model for drilling fluid filtrate damage in two-phase percolation for cement slurry invasion into the reservoir. 17Fan et al. applied material balance theory to comprehensively consider the influence of geological parameters and construction parameters on the damage depth of drilling fluid and established a model that can predict the invasion depth of drilling fluid particles. 18ang et al. established a model for predicting the dynamic damage of drilling fluid filtrate and solid particles through API filtration experiments and laboratory core contamination experiments, which considered the existence of internal mud cake. 19Chen et al. established a model that can predict the formation of mud cake, which assumes that the mud cake forms a filter cake belt near the wellbore without invading the reservoir. 20Lyu et al. found that the main factors affecting the invasion depth of drilling solids and filtrate into the reservoir were mud cake permeability, drilling fluid soaking time, and drilling fluid density by studying the pollution characteristics of drilling solids. 21he reservoir skin factor can quantitatively characterize the contamination of drilling and completion fluids in the reservoir, mainly through the Frick-Economides model, Furui-Zhu-Hill model, and Goode model.Malekzadeh and Tiab introduced the equivalent horizontal section length to characterize the impact of drilling and completion fluid contamination on productivity through well test data, and divided the total skin factor into pseudoskin factor and mechanical skin factor. 22Furui et al. improved the Frick-Economides model and established a model for solving the comprehensive skin factor through equal volume transformation. 23Liu et al. improved the method of Malekzadeh's research, considering the effects of horizontal well section length and anisotropy on the mechanical skin factor. 24However, the equivalent horizontal section length cannot locally characterize the specific contamination at different locations in the horizontal section, but can only characterize the contamination of the entire well section.Li et al. established a skin factor calculation model under segmented acidification conditions, which considered the impact of residual acid flowback on gas percolation near the wellbore after acidification. 25s the development of well types for low permeability reservoirs shifts from vertical to highly inclined/horizontal wells, targeted studies of oil and gas reservoir damage must be conducted for such well types to improve the science and effectiveness of acidification conversion.The wellbore structural properties of horizontal wells greatly increase the oil spill area of oil and gas reservoirs, providing an unrivaled advantage over vertical wells.However, the heterogeneity of oil and gas reservoirs is strong, with natural fractures and caves developing locally.The horizontal profiles are long and the physical properties of the reservoir vary considerably between the profiles.Drilling and completion fluid immersion times and pressures vary, which can easily lead to an irregular distribution of damage severity, adding to the complexity of reservoir heterogeneity.Since acid liquids tend to enter low-permeability, low-damage areas with low flow resistance, the amount of acid entering heavily damaged areas is small, resulting in unsatisfactory acidification effects.Another major reason for the poor acidification effect is the failure to form a high-conductivity main wormhole channel in the acid-affected region.Therefore, efficient acid distribution and efficient wormhole deep penetration are two key techniques to achieve uniform reservoir plug removal and ensure acidification effects in horizontal wells in low-permeability carbonate reservoirs.

| A NONUNIFORM DAMAGE MODEL FOR HORIZONTAL WELL RESERVOIRS
The length of the horizontal wellbore section exceeds that of the vertical well, resulting in increased residence time and contact area between the working fluid and reservoir, thereby elevating the risk of contamination.Additionally, variations in soaking time and pressure of drilling and completion fluids, along with specific damage zone shapes, further contribute to this issue.Particularly for carbonate reservoirs, significant discrepancies exist in reservoir properties across different sections of the wellbore, intensifying irregularities in distribution and severity of damage areas while complicating uneven damage patterns.Therefore, it is imperative to investigate contamination levels and characteristics in horizontal wells, establish clear objectives for acidification and plug removal processes, and implement targeted acid distribution to provide theoretical guidance for selecting appropriate acidification procedures and parameter designs in horizontal wells.By combining a variable skin factor model with a dynamic mud cake formation model, a refined dynamic description model is developed to address heterogeneous damage within horizontal well reservoirs.This comprehensive model comprises four components: a radial mud cake dynamic formation model; a damage radius model; a permeability distribution model; and a heterogeneous skin factor model specifically tailored for horizontal wells.

| Radial filter cake model
During drilling, the invasion of drilling fluid filtrate into the formation occurs due to pressure differential, resulting in the formation of an invasion zone, while solid particles precipitate and accumulate on the wellbore wall, forming a mud cake.In overbalanced drilling operations, both solids and liquids penetrate into the reservoir, leading to a reduction in reservoir permeability and causing damage.Accurate quantification of reservoir damage is crucial for predicting oil and gas well productivity.The extent of reservoir damage in horizontal wells primarily relies on factors such as drilling duration, distribution of filtrate, changes in permeability around the wellbore, and overbalanced pressure differential.

Physical model:
During the drilling process, the drilling fluid filtrate continuously leaks into the reservoir, and the solid particles accumulate on the wellbore to form a filter cake.After a certain period of time, the deposition rate and stripping rate reach equilibrium, forming a stable thickness of filter cake.In the radial direction perpendicular to the horizontal section, there are three parts, from the wellbore outward, namely, the mud cake area, the invasion zone, and the original formation, as shown in Figure 1.
Assumptions of model: The reservoir pressure is constant.The temperature is constant.Ignoring the effect of gravity.The single-phase and radial filtration of drilling fluid obeys Darcy's law.Both particles and filtrate are incompressible, and the fluid viscosity and permeability in the invasion zone remain unchanged.The mud cake only attaches to the wellbore and does not enter the reservoir.

Mathematical model:
The formation rate of mud cake equals the sedimentation rate minus the erosion rate, where the sedimentation rate depends on the pressure gradient of the filtration layer and the mud cake layer, and is a function of fluid flow rate, while the erosion rate depends on the shear stress of the working fluid flowing on the mud cake surface.As the filter cake gradually thickens, the formation rate gradually decreases until the sedimentation and erosion processes reach a steady state, at which point the mud cake thickness remains constant.
Solid particle deposition rate: where R S is solid phase particle stacking rate, g/(cm 2 s); k solid is solid phase particle deposition coefficient; ρ f is the working fluid density, g/cm 3 ; u is the flow rate of filtrate, cm/s; B P is the mass fraction of solid particles in drilling fluid; k e is the erosion coefficient of mud cake, g/(N s); τ cr is the critical shear stress of the mud cake, Pa; and τ s is the shear stress of the working fluid on the mud cake, Pa.The conservation of mass occurs during the deposition of solid particles to form a mud cake where ϕ c is the porosity of mud cake, ρ p is the density of solid particle in the drilling fluid, g/cm 3 , and r c is the radius of drilling fluid invasion, cm.Substituting Equation (1) into Equation ( 3), the mud cake thickness can be solved after integration where r w is the wellbore radius, cm.
As the drilling fluid flows back upwards, it will exert a shear stress on the mud cake.If the flow pattern of the drilling fluid in the annulus is laminar flow, the magnitude of the radial shear stress is determined by the following equation: where v is the drilling fluid flow rate in the annulus, m/s; k′ is the consistency coefficient of drilling fluid, Pa s n' ; and n′ is the flow index of drilling fluid.The fluid flow during the filtration process comprises three parts: the flow of working fluid within the mud cake, the flow of working fluid in the reservoir, and the flow of crude oil in the production zone.Using the method of equivalent percolation resistance, we obtain the expression for the filtration flow rate of the working fluid under radial conditions by performing an equivalent transformation where q is the working fluid filtration rate, m/s; ∆P is the pressure difference between bottom hole pressure and reservoir pressure, MPa; K 0 is the formation permeabil- ity, 10 −3 μm 2 ; K f is the mud cake permeability, 10 −3 μm 2 ; | 1665 μ o is the formation crude oil viscosity, mPa s; μ f is the working fluid viscosity, mPa s; r w,eq is the wellbore radius and equivalent wellbore radius, m; r e,eq is the equivalent flow outer boundary, m; r d,eq is the equivalent filtrate invasion radius, m; ∆l is the length of each small horizontal well section, m; B is the coefficient related to the unit.According to the law of radial flow in plane, the flow velocity of the filtrate at the mud cake can be expressed as The cumulative filtration loss is where Q is the accumulated filtration rate of working fluid per unit formation thickness, m 3 ; T is the soaking time, s.

| Reservoir damage radius model
The radius of reservoir damage can be calculated using the principle of conservation of volume.If each small damage zone in the horizontal section is assumed to be a cylinder with its axis parallel to the well's axis, the volume of such a cylinder can be expressed as The volume of the cylinder can also be represented by the amount of intrusive fluid where Q is the accumulated filtration rate of drilling fluid, m 3 ; ϕ is the formation porosity.Solving the above two equations comprehensively, we can obtain the conversion radius of the damage zone in each small horizontal segment at different times, r d,eq : or wi (11)   The horizontal damage radius of horizontal wells considering reservoir heterogeneity can be calculated according to the following formula, r dH : 2.3 | Permeability distribution model

Model assumptions:
The distribution of permeability in polluted areas follows an exponential relationship.
The fluid seepage in the damage zone meets the Darcy flow.
The fluid is single-phase incompressible.2. Mathematical model: where K d is the permeability of formation damage zone, 10 −3 μm 2 ; r d is the radius of the formation damage zone, m; r c is the radius of the wellbore to which the mud cake is attached, m, Substitute ( 14) into ( 13) and obtain the expression formula for permeability at different radial distances r within the damage range where K c is the mud cake permeability, 10 where P is the formation pressure, MPa; B is the formation volume factor; μ is the fluid viscosity, mPa s.
Integrating both sides of formula ( 16) yields where P e is the formation pressure, MPa; P w is the bottom hole pressure, MPa.
If K is a constant value, it can also be obtained from Equation ( 17 By combining Equations ( 17) and ( 18), the equivalent permeability k dH,eq in the horizontal direction can be obtained ) Based on the research of Frick and Economides et al. 14 and Furui et al. proposed the Furui-Zhu-Hill model. 23The degree of reservoir damage is greater at the heel end of the horizontal well and smaller at the toe end, but due to the influence of heterogeneity, there are fluctuations in some areas (as shown in Figure 1).The heterogeneity skin factor of the horizontal well reservoir is divided into two key parts: (1) the local skin factor affected by formation heterogeneity, which describes the distribution characteristics of the damage in the y-z plane.When the degree of damage is low, the shape of the damage zone is roughly circular.When the invasion range expands, the shape of the damage zone is approximately elliptical due to the influence of various heterogeneity factors of the reservoir.(2) Considering the distribution of the skin factor along the wellbore, it describes the segmented distribution characteristics of the damage along the horizontal wellbore.The degree of damage is determined by various factors such as the permeability and soaking time at different segments.
Model assumptions: (1) The geological model is simplified as a box-shaped reservoir; (2) under the hydraulic drive mode, the fluid in the formation is a single-phase, steady-state flow, in accordance with Darcy's law; (3) the anisotropy index in the damage zone is equal to that of the original formation; (4) the reservoir is anisotropic, where k V represents the vertical permeability and k H represents the horizontal permeability; (5) the gravitational effect of the fluid flow in the formation is disregarded.

Mathematical model:
Referring to the Peacema method, using conformal transformation to equate anisotropic reservoirs to isotropic reservoirs, an equivalent formula for calculating the average length of elliptical damage zones can be obtained where ρ is the conformal transformation variable.B is the conformal transformation constant.It can be obtained from the following equation: For elliptical damage zones The above equation can also be written as where r dH is the radius of the elliptical damage zone in the horizontal direction, m; r w,eq is the equivalent wellbore radius, m; I ani is the anisotropy index of formation, I K K = / ani H V .The equivalent wellbore radius can be expressed as w,eq w ani ani (24)   Using the same conformal transformation to perform an equivalent transformation on the original formation's liquid supply area, obtain the equivalent liquid supply radius, r : | 1667 For anisotropic reservoirs, the skin factor formula is d,eq w,eq (26) Based on the assumed conditions: where K H is the horizontal original permeability of the formation,10 −3 μm 2 ; K V is the vertical original permeability of the formation, 10 −3 μm 2 ; K dH is the horizontal permeability of formation damage zone, 10 −3 μm 2 ; K dV is the vertical permeability of formation damage zone, 10 −3 μm 2 .The skin factor considering reservoir anisotropy is ultimately calculated using the following equation: w,eq (28) 3. Solution of the nonuniform damage model for horizontal wells: The horizontal segment of total length L is divided into several small segments of length Δl, and the skin coefficient of each segment is iteratively solved to evaluate its injury severity.For each segment: 1. Divide the drilling fluid soaking time corresponding to each small horizontal section into n subsections, with a step size of Δt. 2. Apply initial conditions (a) and (b) to each time point.3. Solve the cumulative filtration Q(i) by Equation ( 8). 4. Solve the filtration flow rate u(i) and the converted damage radius r d,eq (i) generated by initial filtration loss through Equations ( 7) and ( 11), respectively.
5. Using the mud cake thickness formulas ( 4) and ( 5), obtain the updated wellbore radius r c (i). 6. Use Equation ( 6) to obtain the updated drilling fluid filtration rate q(i).7. Return to step 3 and start calculating the parameters for the next period.Repeat until q(i) < q(i + 1), at which point the mud cake thickness r cstable and constant fluid loss q stable are obtained at dynamic equilibrium.8. Use Equations ( 8) and (11) to continue solving for the cumulative fluid loss Q and the equivalent damage radius r d,eq until the end of the soaking time, to obtain the final equivalent damage radius r d,eq .9. The horizontal damage radius r dH is obtained from Equation ( 12). 10.Solve the permeability distribution Equation ( 19) to obtain the equivalent permeability k d,equal in the horizontal direction of this small segment.11.The skin coefficient of the small horizontal segment is obtained from the nonhomogeneous skin coefficient equation (28).12. Repeat the above steps to solve for other subsegments to obtain the distribution of skin factors along the horizontal well section.

| CASE CALCULATION AND SENSITIVITY ANALYSIS
Well A is a horizontal well used for evaluating reservoirs.Taking this well as an example, the above model is applied to calculate and analyze the skin factor distribution along the horizontal wellbore.The basic data of Well A is shown in Table 1.By simulating the pollution process caused by mud filtration, we obtained a nonuniform distribution of the skin factor along the damage zone in the horizontal well section, considering the heterogeneity of the reservoir.To explore the specific impact of various factors on the damage, a sensitivity analysis was performed on several key factors using the single-factor variable method.

| Permeability sensitivity analysis
The original permeability of the formation significantly impacts the extent and morphology of damage.The sensitivity analysis of the permeability of the reservoir encountered by Well A comprises two parts: the sensitivity analysis of the spatially nonuniform distribution of permeability along the horizontal well section and the sensitivity analysis of the anisotropy of permeability.

Sensitivity analysis of permeability anisotropy:
According to Figure 2, various horizontal permeability and vertical permeability ratios are employed to characterize the anisotropy of the reservoir, and the damage distribution difference between anisotropic and isotropic reservoirs is analyzed by comparison.The simulation results indicate that anisotropic reservoirs are more susceptible to damage than isotropic reservoirs.As the level of anisotropy increases, the extent of damage to the reservoir decreases.The primary reason for this is that in anisotropic reservoirs, the drilling fluid is more likely to enter the horizontal direction of high permeability, whereas the vertical direction of low permeability is less damaged, creating a pathway for reservoir fluid to reach the wellbore.the wellbore near the isotropic reservoir is completely blocked, preventing fluid flow into the wellbore, leading to severe damage.Figure 3 also demonstrates that the influence of soaking time on permeability anisotropy has an amplifying effect.Specifically, the difference in skin factors gradually increases from the toe to the heel of the horizontal section with increasing soaking time.However, the overall difference is not significant, which indicates that the relationship between the damage degree and permeability anisotropy is weak.

Sensitivity analysis of spatially nonuniform permeability distribution:
Figures 3, 4, and 5 demonstrate the distribution of skin factor when the permeability varies uniformly along the horizontal well axis.The permeability remains constant in Figure 4, and the final simulation results indicate that the damage zone takes the form of a conical frustum, with one end large and the other end small.The primary cause of this outcome is that the reservoir F I G U R E 5 Distribution of skin factor as permeability gradually increases along the horizontal well section.Figures 5 and 6, it is evident that the skin factor is highly affected by the initial formation permeability, and the gradually increasing permeability distribution along the horizontal section significantly widens the damage gap between the heel and toe ends of the horizontal section.The gradually decreasing permeability distribution along the horizontal section diminishes the impact of soaking time, resulting in a relatively uniform damage distribution.
Figures 6 and 7 demonstrate the distribution of skin factors when the permeability varies irregularly along the horizontal well axis.The skin factor is significantly influenced by permeability, and the harm caused by high-permeability areas is much more severe than that caused by other areas.This is because the higher the permeability, the more mud enters the formation, ultimately leading to contamination. Figure 6 demonstrates that the high permeability zone causes significantly more damage than the reservoirs on both sides, whereas, in Figures 7 and 8, the low permeability zone causes significantly less damage than the reservoirs on both sides.Figure 9 illustrates the variation of skin factor with respect to the horizontal permeability of the formation at various soaking times.It is observed that, other things being equal, the skin factor rises almost linearly as permeability increases.Under the same conditions, the skin factor also increases with the increase in soaking time.The slope of the curve in the figure increases with the increase in soaking time, indicating that the difference in skin factor caused by permeability differences gradually widens with time.This suggests that permeability and soaking time have a synergistic effect on the damage.

| Porosity sensitivity analysis
Figures 10 and 11 depict the simulation outcomes on the impact of porosity distribution on the extent and degree of damage.Uniformly and nonuniformly distributed porosity, with three high-porosity zones, while other conditions remain unchanged.The higher the porosity of the reservoir, the smaller the skin factor due to the stage retardation effect in the pores, which is the main cause of damage.The retardation effect at the stage of large pores  is relatively weak, resulting in relatively minor damage.The figure also illustrates that, whether the porosity distribution is uniform or nonuniform, the entire damage zone has a large toe end and a small big toe end along the horizontal section.This suggests that the degree of damage is relatively insensitive to the initial porosity of the formation.Figure 12 shows that the soaking time has a synergistic amplification effect on porosity, resulting in a steeper curve slope as the soaking time extends.As the porosity increases, the curve gradually flattens, indicating that a smaller porosity corresponds to a greater sensitivity of the skin factor to it.

| Sensitivity analysis of pressure difference
During the drilling process, the drilling fluid enters the reservoir under the pressure difference between the reservoir and the wellbore.Because the mud cake and the formation have a significant difference in permeability, the mud cake will cause a substantial resistance to the filtration loss of the drilling fluid.At the beginning, no mud cake forms, resulting in very low filtration resistance.The drilling fluid filtrate enters the reservoir quickly, while the solid particles accumulate on the wellbore and form a mud cake.As the immersion time increases, the thickness of the mud cake also rises, leading to an increase in filtration resistance and a decrease in filtration rate.Additionally, the deposition of solid particles decreases, eventually leveling off with the solid particles being eroded by flow action.At this point, both the filtration rate and the mud cake thickness tend to remain constant.According to Figures 13 and 14, the filter cake thickness and filtration rate of the drilling fluid increase as the drilling pressure differential rises.To examine the influence of pressure differential on the skin factor, it is assumed that the permeability and porosity of the formation along the horizontal section are constant.According to Figure 15, as the pressure differential decreases, the number of solid particles deposited on the filter cake surface decreases, along with the thickness of the mud cake and the skin factor.It is widely believed that the sensitivity of the damage degree to the pressure differential is high, and therefore, the drilling pressure differential should be carefully managed to minimize the pollution damage caused by the working fluid to the formation.

| Sensitivity analysis of annular flow velocity
As illustrated in Figures 16 and 17, when the annulus fluid is static (flow velocity is 0), it can be considered as a curve under static filtration conditions.Currently, there is no erosion occurring within the mud cake, resulting in the production of a thicker mud cake than the stable mud cake thickness observed with annular flow velocity.As the ring flow velocity increases, the erosion effect of the drilling fluid on the filter cake intensifies, resulting in a decrease in the stable mud cake thickness at dynamic equilibrium.
According to Figure 17, the equilibrium filtration rate is relatively low when the annulus velocity is 0, which represents static filtration.As the annulus velocity increases, the filtration rate at dynamic equilibrium also increases, with the increase gradually becoming more significant.As the annular velocity increases, the mud cake's thickness decreases, reducing the resistance to the invasion of the working fluid into the reservoir, resulting in an increase in the speed of the working fluid entering the reservoir.To investigate the impact of filter cake permeability on the skin factor, it is assumed that the horizontal section's spatial distribution of formation permeability and porosity remains constant.According to Figure 18, the skin factor escalates as the annulus flow rate rises.This is due to the increase of shear force on the mud cake with the increase of the annulus flow rate, which leads to an increase in the corresponding filtration rate at dynamic equilibrium, that is, the accumulation of filtration into the reservoir increases the radius of the damage zone, causing an increase in the skin factor.It is believed that the degree of damage is highly sensitive to the annulus flow rate.Strata with isotropic permeability are more vulnerable to damage than anisotropic strata; as the level of anisotropy increases, the extent of formation damage decreases.The effect of drilling fluid immersion time on permeability anisotropy is amplified, which means that the difference between skin factors gradually increases as the immersion time increases from the toe to the heel of the horizontal section.However, the overall difference is not significant, indicating that the sensitivity of reservoir damage to permeability anisotropy is weak.
The higher the porosity of the reservoir, the smaller the skin factor of the reservoir to the stage retardation effect in the pores, which is the main cause of damage.However, the stage retardation effect in large pores is relatively weak, resulting in relatively light damage.The reservoir damage zone exhibits a considerable heel and negligible toe along the horizontal section, which suggests that the sensitivity of the reservoir damage degree to the original porosity of the reservoir is low.As the pressure difference for drilling increases, both the thickness of the filter cake and the filtration rate of the drilling fluid also increase.As the pressure differential decreases, the mass of solid particles deposited on the surface of the filter cake reduces, leading to a decrease in the thickness of the mud cake, and consequently, the skin factor is also reduced.The degree of reservoir damage is highly sensitive to the drilling pressure differential, and it should be controlled as much as possible to minimize the damage caused by the working fluid to the formation.The skin factor of the reservoir increases as the annulus flow rate increases, primarily due to the increased shear effect on the mud cake.As a result, the dynamic equilibrium filtration rate increases, leading to a higher cumulative filtration into the reservoir and a larger damage zone radius, ultimately leading to a further increase in the skin factor.The degree of reservoir damage is highly sensitive to the annulus flow rate.Therefore, it is crucial to control the flow rate of the working fluid during drilling to minimize the damage to the reservoir.

AUTHOR CONTRIBUTIONS
Shijing Xu and Guoqing Wang were involved in conceptualization, methodology, resources, writingoriginal draft preparation, writing-review and editing, and funding acquisition.Bin Gao contributed to software and investigation.Shijing Xu contributed to validation and formal analysis.Jiaxin Tian was involved in visualization and project administration.All authors have read and agreed to the published version of the manuscript.
U R E 1 Radial distribution of drilling fluid invasion damage zone.XU ET AL.

F I G U R E 2
Distribution of skin coefficient with different degrees of permeability anisotropy.F I G U R E 3 Distribution of skin factor when permeability remains constant along the horizontal well section.F I G U R E 4 Distribution of skin factor as permeability gradually decreases along the horizontal well section.

F I G U R E 6
Distribution of skin factor at high permeability in the middle section of the horizontal section.F I G U R E 7 Distribution of skin factor at low permeability in the horizontal section.

F I G U R E 8
Distribution of skin coefficient in horizontal sections with three high permeability zones.F I G U R E 9 trend of skin coefficient in horizontal permeability of different layers under different soaking times.

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I G U R E 10 Distribution of skin coefficient in horizontal section with uniform porosity distribution.F I G U R E 11 Distribution of skin coefficient in the horizontal segment with three high porous zones.F G U R E 12 Trend of skin coefficient variation with formation porosity under different soaking times.F I G U E 13 Impact of drilling pressure difference on mud cake thickness.XU ET AL.| 1671

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I G U R E 14 Impact of drilling pressure difference on the filtration rate of working fluid.F I G U R E 15 Effect of different pressure differences on skin coefficient.F I G U R E Effect of annular velocity on mud cake thickness.F I G U R E 17 of annular flow rate on the filtration rate of fluid.F I G U 18 of annular velocity on reservoir skin coefficient.Taking into account the formation of mud cake and the dynamic damage factors caused by drilling fluid on the reservoir during horizontal well drilling, a refined dynamic description model for nonuniform damage in horizontal wells was established.The coupled simulation accounted for the dynamic damage changes of the reservoir skin factor and the dynamic generation of mud cake.The coupled model comprises a radial mud cake dynamic formation model, a reservoir damage radius model, a permeability distribution model, and a horizontal well nonuniform skin factor model.It captures the dynamic evolution of reservoir damage caused by drilling fluid contamination during horizontal well drilling, and provides a real-time representation of changes in the reservoir skin factor of horizontal wells, measuring the depth and extent of radial reservoir damage.